Question

The LCM of three numbers is 2400. If the numbers are in the ratio of 3 : 4 : 5, find the greatest number among them.

• A. 200
• B. 160
• C. 250
• D. 120

Answer 1

Answer:

A. 200

The greatest number among them is 200.

• Assume the numbers based on the ratio:
  Let the three numbers be $3x$, $4x$, and $5x$, where $x$ is their Highest Common Factor (HCF).

• Find the LCM of the numbers in terms of $x$:
  The Least Common Multiple (LCM) of the coefficients 3, 4, and 5 is:
  $3 \times 4 \times 5 = 60$
  Therefore, the LCM of $3x$, $4x$, and $5x$ is $\mathbf{60x}$.

• Solve for $x$:
  Given that the LCM is 2400:
  $60x = 2400$
  $x = \frac{2400}{60} = \mathbf{40}$

• Find the greatest number:
  The largest number in the ratio is $5x$:
  $5 \times 40 = \mathbf{200}$